Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch

Sunday, March 21, 2010

Notes to My Dad

My father Paul Fortnow passed away thirty years ago today. Five years ago I wrote about some of the lessons I learned from him.

Suppose I could go contact him back into time. What would I tell him?

I could tell him about his beautiful granddaughters.

I could tell him that his Red Sox won another world series in 2007 but some things don't change, it's the Yankees who are reigning champs.

I could tell him about a device in my pocket called an "iPhone" that lets me contact anyone, access nearly all public information and it plays music and movies too. A big improvement over the Sony Walkman.

I could tell him about how easily we can search for the most trivial information. I learned that he wrote a review article when I was just a baby, that the house he grew up in was torn down and replaced with the Marshfield city hall, and that he died just about the same time that JR was shot.

I could tell him the answer to the biggest mystery of his generation: FBI Agent Mark Felt was Deep Throat.

But most of I would tell my father that taking one children's aspirin every day reduces the risk of heart attacks and maybe, just maybe, I'd be telling him these things in person.

3 comments:

Yesterday my wife, my sons, and I scattered the ashes of a beloved 97-year-old aunt into the waters of her favorite Puget Sound beach. In honor of Aunt Marie, this essay is offered, written to her from 30 years hence.

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To: Marie (in 2010)From: Marie's family (in 2040)

Marie, you passed away thirty years ago. Suppose we could go and contact you back into time. What would we tell you?

Here's what the three decades from 2010-40 have brought us.

Of the Clay Millenium Prizes, the only one solved in the last thirty years is P versus NP. It turns out to be provably true that NP includes problems that are not in P.

But on the other hand ... it also turns out to be provably true that no concrete NP-complete problem has a proof (checkable in PTIME) that it is not in P ... and so we are still looking for concrete examples.

Related methods have established that neither classical nor quantum systems dynamical system can be simulated with PTIME resources. But on the other hand ... it turns out that both classical and quantum thermostatic simulation is in P ... and experimental physicists have yet to construct a scalable non-thermostatic quantum dynamical system.

So the dream of quantum computing is still alive ... and yet we can reliably simulate every system in nature.

In terms of fundamental theory, we now understand M-Theory as being the unique causally separable, relativistically invariant, finite-temperature quantum field theory that can be simulated with classical computational resources.

But on the other hand ... since M-theory is itself not a constructive field theory, the Yang-Mills Clay Prize is still (formally) open.

As for the four other Clay Prizes (Birch and Swinnerton-Dyer Conjecture, Hodge Conjecture, Navier-Stokes Equations, and Riemann Hypothesis), they are *all* still open!

The upshot of all these advances is that we now observe, simulate, and manipulate the nano-scale in the ``exacting sense'' of von Neumann's 1948 vision: "the exacting sense in which one may want to understand a detailed drawing of a machine, i.e., finding out where every individual nut and bolt is located."

This crossover has launched the three largest enterprises in human history: (1) the planetary biome survey project, (2) the planetary biome restoration project, (3) the human regenerative healing project. The end of the 21st Century will see ten billion people living on our planet ... and nowadays (in 2040) we contemplate that prospect with sober confidence that both the planet and the people on it will be in pretty good shape.

Indeed, our main problem is 2040 is that we have too many jobs ... because there is too much productive work ... for even our planet's two billion young people to do. In 2040 it appears that about 1/300 young adults wishes to become mathematician, engineer, or scientist ... and we wish that number were 1/100.

The greatest change of all---in 2040 as contrasted with 2010---has been in the academic literature. Academia has spontaneously reorganized itself into "gardens" instead of "disciplines", so that nowadays, professors and students spend much of their time cultivating their gardens (very much in the spirit of Voltaire).

In practice this has turned out to mean, that the mission of academia is to curate the shared documentation of the world---and to participate in the ongoing construction of well-founded narratives about that world---of which this cheerful time-traveling letter is one expression.

Most of all, we want to tell you that your beautiful great-great grand-nieces and nephews are just now entering into their adult life. Thank you, Marie, for helping them to be born into this most hopeful, beautiful, and amazing of centuries!

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Note: Marie had an intense interest in mathematics, science and engineering; she would have been very well satisfied to know this world was coming.